sci.physics.research

On Sat, 1 Sep 2007 19:54:05 +0000 (UTC), Benjamin wrote:

> Jim Black wrote:
>
>> I agree that if you calculate P+- with the polarizers aligned using the
>> authors' model, you get 1/8. But if you do the experiment, you find that
>> P+- is (within experimental error) zero.
>
> Have you actually done such an experiment?
> I think one can read from Aspect,
>
>> Physical Review Letters 49, 91 (1982),

They write:

However, all previous experiments involved single-channel analyzers,
transmitting one polarization (a or b) and blocking the orthogonal one.

>> The measured quantities were thus only the coincidence rates in +1
>> channels: R++(a;b). Several difficulties then arise as a result of
>> the very low efficiency of the detection system (the photo multipliers
>> have low quantum efficiencies and the angular acceptance is small).
>> The measurements of polarization are inherently incomplete: When a
>> pair has been emitted, if no count is obtained at one of the
>> photomultipliers, there is no way to know whether it has been missed
>> by the (low efficiency) detector or whether it has been blocked by
>> the polarizer (only the latter case would be a real polarization
>> measurement). Thus, coincidence counting rates such as R+-(a;b) or
>> R--(a;b) cannot be measured directly.

[...]

In this Letter, we report the results of an experiment following much
more closely the ideal scheme of Fig. 1. True dichotomic polarization
measurements on visible photons have been performed by replacing
ordinary polarizers by two-channel polarizers, separating two orthogonal
linear polarizations (Fig. 2).

[...]

Using a fourfold coincidence technique, we measure in a single run the
four coincidence rates R +/- +/- (a,b), yielding directly the
correlation coefficient for the measurements along a and b:

E(a,b) = \frac{R++(a,b) + R--(a,b) - R+-(a,b) - R-+(a,b)}
{R++(a,b) + R--(a,b) + R+-(a,b) + R-+(a,b)}.

> Has this, what Aspect wrote here, changed?

It changed when Aspect did the experiment you cite. The weakness he was
describing was inherent in *previous* experiments. However, even those
previous experiments would have been enough to falsify Fritsche and Haugk's
model, because Fritsche and Haugk have P++ = 1/8 when the polarizers are at
right angles to each other.

Notice that Figure 3 of Aspect et al. shows a correlation of nearly +1 when
the polarimeters are aligned. That means that the polarization of the
photons detected was almost always the same. In Fritsche and Haugk's
model, the polarizations are different 25% of the time, but they
nevertheless compute a correlation coefficient of +1 (Eq. 17) -- which is
obviously wrong. I don't know how they got Equation 16, but when I compute
the correlation coefficient according to their model, I get one-half their
result. Their Equation 16 certainly doesn't agree with Aspect et al.'s
Equation 1, which uses joint, not conditional probabilities. Nor does it
agree with Aspect et al.'s Equation 3, what they actually measured, which
will clearly equal Equation 1 in the ideal case of 100% efficiency.

Here's a paper from another experiment that actually shows a plot of the
coincidence rates:

/abs/quant-ph/9810080

Note that in this case, they've set up the experiment so that the photon
polarizations at the detectors are anticorrelated, but you could account
for that in Fritsche and Haugk's model by just switching the sine and
cosine in Eq. 7; all you'll get is a few sign changes. Fritsche and
Haugk's model predicts a minimum coincidence rate that is 1/3 the maximum
coincidence rate. Quantum mechanics predicts a minimum coincidence rate of
zero for an ideal experiment, but of course a real experiment will not be
perfect. (For example, in Weihs et al., one source of error was the not
perfectly-rectangular electrical signal controlling the polarization
direction measured.) Figure 3 of Weihs et al. shows the measured
coincidence rates, which are clearly inconsistent with the 1/3 ratio from
Fritsche and Haugk's model.

--
Jim E. Black